Field of the Invention
The invention relates generally to the field of signal processing. More specifically, the invention is related to methods, systems, and program code for filtering noise and restoring attenuated spectral components in signals.
Description of the Related Art
Signals in the form of acoustic wave (acoustic signals), for example, generated by an acoustic wave source can travel through various materials including reservoir and non-reservoir rock, well tubulars including drilling pipe, and other drilling equipment including the drilling bit. Acoustic signals generally lose their accuracy due to the accompanied background noise during transmission and recording. The background noise is composed of two parts, an internal part which is generated from the measurement system, and an external part which comes from the surround environment.
Acoustic signals may also be distorted during transmission and recording due to the attenuation of the signal, particularly the high frequency components. Attenuation of the amplitude spectrum of an acoustic signal is generally non-uniform. The higher the frequency of the spectral components of the acoustic signals, the greater the attenuation of the respective spectral components of the acoustic signals.
As illustrated in FIG. 1A, both background noise and the non-uniform attenuation will combined together to deteriorate the quality of the acoustic signals. FIG. 1A shows an acoustic signal 21 recorded simultaneously using a microphone and an accelerometer. The frequency components 22 of a sample recorded by the accelerometer represent an un-attenuated version of frequency components of the sample of the audio signal; i.e., what they should have been but for the attenuation. It can be seen here that the high-frequency components of the acoustic signal 21 recorded by the microphone are attenuated down to the level of noise.
To increase the quality of the signals, the deteriorated signals should be filtered to remove noise and their attenuated spectral components should be restored. There are two common approaches: frequency filtering and amplitude filtering. Frequency filtering is to remove from a signal some unwanted frequency components by using an electronic device or a mathematical process. In this approach, any frequency components with frequency greater and/or less than preselected cutoff values are removed or heavily attenuated.
When a mathematical process employed, signals in time domain (e.g., graphically illustrated as signal amplitude over time) are converted to the frequency domain to represent the signals in the amplitude spectrum. This is accomplished, for example, through use of the Fast Fourier Transformation (FFT). FIG. 1A illustrates an example of a pair of acoustic signals, existing in the time domain, being converted into the frequency domain. With the signal converted into the frequency domain, the signal components in the amplitude spectrum having a frequency above and/or below a cutoff value are removed.
Amplitude filtering is normally a mathematical process in which components in the amplitude spectrum with an amplitude above and/or below a cutoff (threshold) value are removed. If required, an inverse FFT is then performed on the filtered frequency domain signal to recover the time domain output signal.
In these two approaches, proper cutoff (threshold) values are critical. It is not always the case, however, that there exist clear cutoffs usable to separate the acoustic signals from the noise. FIG. 1B illustrates an example of a restored signal (solid line) where the amplitude cutoff threshold was too low, which resulted in excessive filtering. FIG. 1C illustrates an example of a restored signal (solid line) where the amplitude cutoff was too high, which resulted in excessive noise remaining and amplified in the restored signal.
Some relatively sophisticated techniques have been proposed to filter noise by using “Spectral Subtraction” methodology, e.g. S. F. Boll: “Suppression of Acoustic Noise in Speech Using Spectral Subtraction”, IEEE Trans. on Acous. Speech and Sig. Proc., 27, 1979. pp. 113-120; and U.S. patent 2007/0255560 A1, titled “Low Complexity Noise Reduction Method”. In this type of approach, the noisy signals are filtered by subtracting the spectral noise bias. In the first example, the spectral noise is calculated during non-speech activity. In the second example, the spectral noise is estimated from a “Noisy Activity Detector” procedure. This type of approach, however, would be difficult to apply to situations in which the noise properties are unknown, such as, for example, those associated with drilling operations, to include drilling operations involving real-time steering of the drilling bit.
To further increase the accuracy of acoustic signals, the attenuated spectral components should be restored. U.S. patent 2012/0143604 A1, titled “Method for Restoring Spectral Components in Denoised Speech Signals,” discusses an approach for doing so. This approach, however, requires training undistorted bases obtained from a full-bandwidth clean speech signal. This requirement, therefore, limits the application of the approach to scenarios in which such a full-bandwidth clean signal is available, excluding application of the approach from those scenarios where the full-bandwidth cannot be obtained. U.S. Patent 2004/0122596 A1, “Method for High Frequency Restoration of Seismic Data,” describes an approach in which attenuation of high frequency components is estimated from acoustic signals reflected at consecutive depth levels of formation boundaries. An inverse operator is then determined from the attenuation for each depth level. The determined inverse operators are applied to reflected acoustic signals to restore their attenuated high frequency components. This approach, however, requires knowing the manner in which the high frequency components attenuate.
Each of above mentioned methods or approaches have their merits and specialized area of application. Recognized by the inventor, however, is that there are numerous situations in which acoustic signals cannot be separated from the accompanied noise by some frequency or constant amplitude cutoffs, or clean signal or noise samples, and where the pattern of high frequency component attenuation cannot be obtained.
As noted above, acoustic signals can attenuate during transmission and recording. Under various conditions, some or all of high frequency components of the signals can attenuate to the similar level as background noise. For example, the virgin acoustic (sound) signal generated from an underwater device is both distorted by substantial accompanied background noise that varies with time, and is distorted as a result of attenuation of its high frequency components during transmission through the water. When recorded from a long distance away from the source, the recorded sound will have inherent noise and the sound will be significantly distorted due to the attenuated high frequency components.
Recognized by the inventor is that the situations are similar when recording acoustic signals from a source in distance in air or from underground. Accordingly, the inventor has recognized that common characteristics of these situations include: (1) the background noise may not be constant, and (2) the high frequency components generally will have attenuated significantly by the time the signal reaches to the recording devices. Correspondingly, the inventor has recognized that there exists a need for systems, computer programs, computer readable media, and computer assisted methods to both filter non-constant noise, and then to restore attenuated high frequency components of the filtered signals sufficient to provide a filtered and restored signal, substantially matching the original virgin signal.